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Proof step 10 from proof div-add-pos (previous step)

0 ≤ i1, 0 < j, 0 ≤ j0, j0 < j, 0 ≤ i2 ⊦ ((i2 + i1) * j + j0) / j = i1 + i2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: diveq-pos seq: 0 ≤ i0 * j + j0, 0 ≤ j0, j0 < j ⊦ (i0 * j + j0) / j = i0 subst: [j0, j, i0] → [j0, j, i1 + i2] flags: rewrite, current

Additional information

Used simplifier rules: zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j0, j, i1 + i2